Abstract
Mental abacus is mental arithmetic with the help of an imagined abacus. Children skilled in mental abacus have been shown to exhibit top-quality arithmetic abilities. The current study investigated whether children with high-level mental abacus ability could outperform untrained control children in non-symbolic number sense, which is considered to be fundamental for arithmetic development. One hundred and fifty children (75 children skilled in mental abacus and 75 controls) took part in this study. Children skilled in mental abacus completed a mental abacus level test. The two groups of children performed serial cognitive tasks, assessing non-symbolic number comparison, arithmetic, language, spatial processing, visual perception, attention, processing speed, working memory, and general intelligence. Results showed that children skilled in mental abacus had significantly better non-symbolic number sense than the other children after controlling for general intelligence. The significant difference in non-symbolic number sense remained after controlling for age, gender, all types of cognitive processing available, and arithmetic performance. A mediation model showed that non-symbolic number sense partially mediated the group difference in arithmetic development. These findings suggest that children skilled in mental abacus have enhanced non-symbolic number sense and raise the possibility that mental abacus training could directly improve children’s non-symbolic numerical skills.
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References
Agrillo, C., Piffer, L., & Adriano, A. (2013). Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM. Behavioral and Brain Functions, 9, 14–14. https://doi.org/10.1186/1744-9081-9-26.
Amaiwa, S., & Hatano, G. (1989). Effects of abacus learning on 3rd-graders performance in paper-and-pencil tests of calculation. Japanese Psychological Research, 31(4), 161–168. https://doi.org/10.4992/psycholres1954.31.161.
Anobile, G., Stievano, P., & Burr, D. C. (2013). Visual sustained attention and numerosity sensitivity correlate with math achievement in children. Journal of Experimental Child Psychology, 116(2), 380–391. https://doi.org/10.1016/j.jecp.2013.06.006.
Barner, D., Alvarez, G., Sullivan, J., Brooks, N., Srinivasan, M., & Frank, M. C. (2016). Learning mathematics in a Visuospatial format: A randomized, controlled trial of mental abacus instruction. Child Development, 87(4), 1146–1158. https://doi.org/10.1111/cdev.12515.
Berg, D. H. (2008). Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory, and reading. Journal of Experimental Child Psychology, 99(4), 288–308. https://doi.org/10.1016/j.jecp.2007.12.002.
Bhaskaran, M., Sengottaiyan, A., Madhu, S., & Ranganathan, V. (2006). Evaluation of memory in abacus learners. Indian Journal of Physiology and Pharmacology, 50(3), 225–233.
Barner, D., Athanasopouloua, A., Chua, J., Lewisb, M., Marchanda, E., Schneiderc, R., & Frank, M. (2018). A one-year classroom-randomized trial of mental abacus instruction for first- and second-grade students. Journal of Numerical Cognition, 3(3), 540–558. https://doi.org/10.5964/jnc.v3i3.106.
Boonen, A. J. H., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001.
Bull, R., & Johnston, R. S. (1997). Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65(1), 1–24. https://doi.org/10.1006/jecp.1996.2358.
Chalip, L., & Stigler, J. W. (1986). The development of achievement and ability among Chinese children: A new contribution to an old controversy. Journal of Educational Research, 79(5), 302–307. https://doi.org/10.1080/00220671.1986.10885695.
Chen, C. L., Wu, T. H., Cheng, M. C., Huang, Y. H., Sheu, C. Y., Hsieh, J. C., & Lee, J. S. (2006). Prospective demonstration of brain plasticity after intensive abacus-based mental calculation training: An fMRI study. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment, 569(2), 567–571. https://doi.org/10.1016/j.nima.2006.08.101.
Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163–172. https://doi.org/10.1016/j.actpsy.2014.01.016.
Cirino, M. (2011). Hemingway's "big two-Hearted River": Nick's strategy and the psychology of mental control. Papers on Language and Literature, 47(2), 115–140.
Corsi, P. M. (1972). Human memory and the medial temporal region of the brain. Doctoral Dissertation, Mcgill University.
Cowan, R., & Powell, D. (2014). The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability. Journal of Educational Psychology, 106(1), 214–229. https://doi.org/10.1037/a0034097.
Cui, J., Zhang, Y., Cheng, D., Li, D., & Zhou, X. (2017). Visual form perception can be a cognitive correlate of lower level math categories for teenagers. Frontiers in Psychology, 8, 1336. https://doi.org/10.3389/fpsyg.2017.01336.
Cui, J., Zhang, Y., Wan, S., Chen, C., Zeng, J., & Zhou, X. (2019). Visual form perception is fundamental for both reading comprehension and arithmetic computation. Cognition, 189, 141–154.
Dong, S. S., Wang, C. J., Xie, Y., Hu, Y. Z., Weng, J., & Chen, F. Y. (2016). The impact of abacus training on working memory and underlying neural correlates in young adults. Neuroscience, 332, 181–190. https://doi.org/10.1016/j.neuroscience.2016.06.051.
Donlan, C., & Wu, C. (2017). Procedural complexity underlies the efficiency advantage in abacus-based arithmetic development. Cognitive Development, 43, 14–24. https://doi.org/10.1016/j.cogdev.2017.02.002.
Du, F. L., Chen, F. Y., Li, Y. X., Hu, Y. Z., Tian, M., & Zhang, H. (2013). Abacus training modulates the neural correlates of exact and approximate calculations in chinese children: An fmri study. Biomed Research International, 12. doi:https://doi.org/10.1155/2013/694075.
Ekstrom, R. B. R., French, J. J. W., Harman, H. H., & Dermen, D. (1976). Manual for kit of factor-referenced cognitive tests. Princeton Nj Educational Testing Service.
Frank, M. C., & Barner, D. (2012). Representing exact number visually using mental abacus. Journal of Experimental Psychology-General, 141(1), 134–149. https://doi.org/10.1037/a0024427.
Fuchs, L. S., Fuchs, D., Hamlet, C. L., Powell, S. R., Capizzi, A. M., & Seethaler, P. M. (2006). The effects of computer-assisted instruction on number combination skill in at-risk first graders. Journal of Learning Disabilities, 39(5), 467–475. https://doi.org/10.1177/00222194060390050701.
Fuchs, L. S., Fuchs, D., Compton, D. L., Hamlett, C. L., & Wang, A. Y. (2015). Is word-problem solving a form of text comprehension? Scientific Studies of Reading, 19(3), 204–223. https://doi.org/10.1080/10888438.2015.1005745.
Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43(4), 981–986. https://doi.org/10.3758/s13428-011-0097-5.
Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668. https://doi.org/10.1038/nature07246.
Hanakawa, T., Honda, M., Okada, T., Fukuyama, H., & Shibasaki, H. (2003). Neural correlates underlying mental calculation in abacus experts: A functional magnetic resonance imaging study. Neuroimage, 19(2), 296–307. https://doi.org/10.1016/s1053-8119(03)00050-8.
Hatano, G., & Osawa, K. (1983). Digit memory of grand experts in abacus-derived mental calculation. Cognition, 15(1–3), 95–110. https://doi.org/10.1016/0010-0277(83)90035-5.
Hatano, G., Miyake, Y., & Binks, M. G. (1977). Performance of expert abacus operators. Cognition, 5(1), 47–55. https://doi.org/10.1016/0010-0277(77)90016-6.
Hatano, G., Shimizu, K., & Amaiwa, S. (1987). Formation of a mental abacus for computation and its use as a memory device for digits - a developmental-study. Developmental Psychology, 23(6), 832–838. https://doi.org/10.1037//0012-1649.23.6.832.
Hatta, T., & Miyazaki, M. (1990). Visual imagery processing in Japanese abacus experts. Imagination Cognition & Personality, 9(2), 91–102. https://doi.org/10.2190/43JU-8CBU-1LTY-RY6W.
Hatta, T., & Nishiide, S. (1991). Teachers' stress in Japanese primary schools: Comparison with workers in private companies. Stress & Health, 7(4), 207–211. https://doi.org/10.1002/smi.2460070403.
Hayes, A.F., 2012. Process: A versatile computational tool for observed variable mediation, moderation, and conditional process Modelling [white paper].
Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79(2), 192–227. https://doi.org/10.1006/jecp.2000.2586.
Hedden, T., & Yoon, C. (2006). Individual differences in executive processing predict susceptibility to interference in verbal working memory. Neuropsychology, 20(5), 511–528. https://doi.org/10.1037/0894-4105.20.5.511.
Hishitani, S. (1990). Imagery experts - how do expert abacus operators process imagery. Applied Cognitive Psychology, 4(1), 33–46. https://doi.org/10.1002/acp.2350040104.
Hu, Y., Geng, F., Tao, L., Hu, N., Du, F., Fu, K., & Chen, F. (2011). Enhanced white matter tracts integrity in children with abacus training. Human Brain Mapping, 32(1), 10–21. https://doi.org/10.1002/hbm.20996.
Huang, J., Du, F. L., Yao, Y., Wan, Q., Wang, X. S., & Chen, F. Y. (2015). Numerical magnitude processing in abacus-trained children with superior mathematical ability: An EEG study. Journal of Zhejiang University-Science B, 16(8), 661–671. https://doi.org/10.1631/jzus.B1400287.
Irwing, P., Hamza, A., Khaleefa, O., & Lynn, R. (2008). Effects of abacus training on the intelligence of Sudanese children. Personality and Individual Differences, 45(7), 694–696. https://doi.org/10.1016/j.paid.2008.06.011.
Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58. https://doi.org/10.1016/j.jecp.2013.02.001.
Kawakami, Y., Abe, T., Kuno, S. Y., & Fukunaga, T. (1995). Training-induced changes in muscle architecture and specific tension. European Journal of Applied Physiology & Occupational Physiology, 72(1–2), 37–43.
Ku, Y. X., Hong, B., Zhou, W. J., Bodner, M., & Zhou, Y. D. (2012). Sequential neural processes in abacus mental addition: An eeg and fmri case study. PLoS One, 7(5), 15. https://doi.org/10.1371/journal.pone.0036410.
Kyttala, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23(1), 77–94. https://doi.org/10.1007/bf03173141.
Kyttala, P., Erkkola, M., Lehtinen-Jacks, S., Ovaskainen, M. L., Uusitalo, L., Veijola, R., et al. (2014). Finnish children healthy eating index (FCHEI) and its associations with family and child characteristics in pre-school children. Public Health Nutrition, 17(11), 2519–2527. https://doi.org/10.1017/s1368980013002772.
Li, Y., Chen, F., & Huang, W. (2016). Neural plasticity following abacus training in humans: a review and future directions. Neural Plasticity,2016,(2016-1-4), 2016(3), 1213723. doi:https://doi.org/10.1155/2016/1213723.
Li, Y. X., Wang, Y. Q., Hu, Y. Z., Liang, Y. R., & Chen, F. Y. (2013). Structural changes in left fusiform areas and associated fiber connections in children with abacus training: Evidence from morphometry and tractography. Frontiers in Human Neuroscience, 7, 8. https://doi.org/10.3389/fnhum.2013.00335.
Looi, C. Y., Lim, J., Sella, F., Lolliot, S., Duta, M., Avramenko, A. A., & Kadosh, R. C. (2017). Transcranial random noise stimulation and cognitive training to improve learning and cognition of the atypically developing brain: A pilot study. Scientific Reports, 7, 10–10. https://doi.org/10.1038/s41598-017-04649-x.
Meng, X. (2016). Striding forward in the interweaving of history and reality -- commemorating the 3rd anniversary of the success of the application for world cultural heritage of "Chinese abacus". Abacus and Mental abacus, 6, 5–7.
Menninger, K. (1971). Number words and number symbols: A cultural history of numbers. Mathematical Gazette, 55(393), 480–342. https://doi.org/10.2307/3615053.
Miller, K. F., & Stigler, J. W. (1991). Meanings of skill: Effects of abacus expertise on number representation. Cognition & Instruction, 8(1), 29–67. https://doi.org/10.1207/s1532690xci0801_2.
Na, K. S., Lee, S. I., Park, J. H., Jung, H. Y., & Ryu, J. H. (2015). Association between abacus training and improvement in response inhibition: A case-control study. Clinical Psychopharmacology and Neuroscience, 13(2), 163–167. https://doi.org/10.9758/cpn.2015.13.2.163.
Ni, X. (2007). The revision basis and empirical analysis of the standard of abacus mental calculation in China. Abacus and mental abacus, 2, 38–41.
Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503. https://doi.org/10.1126/science.1102085.
Purpura, D. J., & Ganley, C. M. (2014). Working memory and language: Skill-specific or domain-general relations to mathematics? Journal of Experimental Child Psychology, 122, 104–121. https://doi.org/10.1016/j.jecp.2013.12.009.
Putz, D. A., Gaulin, S. J. C., Sporter, R. J., & McBurney, D. H. (2004). Sex hormones and finger length - what does 2D : 4D indicate? Evolution and Human Behavior, 25(3), 182–199. https://doi.org/10.1016/j.evolhumbehav.2004.03.005.
Rau, P. L. P., Xie, A., Li, Z., & Chen, C. (2016). The cognitive process of chinese abacus arithmetic. International Journal of Science and Mathematics Education, 14(8), 1499–1516. https://doi.org/10.1007/s10763-015-9658-x.
Rohde, T. E., & Thompson, L. A. (2007). Predicting academic achievement with cognitive ability. Intelligence, 35(1), 83–92. https://doi.org/10.1016/j.intell.2006.05.004.
Raven, J., Raven, J. C., & Court, J. H. (1998). Manual for Raven’s progressive matrices and vocabulary scales. Oxford: Oxford Psychologists Press.
Salthouse, T. A., & Coon, V. E. (1994). Interpretation of differential deficits - the case of aging and mental arithmetic. Journal of Experimental Psychology-Learning Memory and Cognition, 20(5), 1172–1182. https://doi.org/10.1037/0278-7393.20.5.1172.
Salthouse, T. A., & Meinz, E. J. (1995). Aging, inhibition, working-memory, and speed. Journals of Gerontology Series B-Psychological Sciences and Social Sciences, 50(6), P297-P306. doi:https://doi.org/10.1093/geronb/50B.6.P297.
Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2016). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 1, 1–16. https://doi.org/10.1111/desc.12372.
Shen, H. (2006). Teaching mental abacus calculation to students with mental retardation. Journal of the International Association of Special Education, 7, 56–66.
Shepard, R. N., & Metzler, J. (1971). Mental rotation of 3-dimensional objects. Science, 171(3972), 701. https://doi.org/10.1126/science.171.3972.701.
Siegel, L., & Ryan, E. (1988). Development of grammatical-sensitivity, phonological, and short term memory skills in normally achieving and learning disabled children. Developmental Psychology, 24(1), 28–37. https://doi.org/10.1037/0012-1649.24.1.28.
So, D., & Siegel, L. (1997). Learning to read Chinese: Semantic, syntactic, phonological and working memory skills in normally achieving and poor Chinese readers. Reading and Writing, 9(1), 1–21. https://doi.org/10.1023/A:1007963513853.
Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology, 13, 290–312. https://doi.org/10.2307/270723.
Stigler, J. W. (1984). “Mental abacus”: The effect of abacus training on Chinese children's mental calculation. Cognitive Psychology, 16(2), 145–176. https://doi.org/10.1016/0010-0285(84)90006-9.
Sullivan, J., Frank, M. C., & Barner, D. (2016). Intensive math training does not affect approximate number acuity: Evidence from a three-year longitudinal curriculum intervention. Journal of Numerical Cognition, 2(2), 57–76. https://doi.org/10.5964/jnc.v2i2.19.
Swanson, H. L., Jerman, O., & Zheng, X. H. (2009). Math disabilities and reading disabilities can they be separated? Journal of Psychoeducational Assessment, 27(3), 175–196. https://doi.org/10.1177/0734282908330578.
Tanaka, S., Michimata, C., Kaminaga, T., Honda, M., & Sadato, N. (2002). Superior digit memory of abacus experts: An event-related functional MRI study. Neuroreport, 13(17), 2187–2191. https://doi.org/10.1097/00001756-200212030-00005.
Tinelli, F., Anobile, G., Gori, M., Aagten-Murphy, D., Bartoli, M., Burr, D. C., et al. (2015). Time, number and attention in very low birth weight children. Neuropsychologia, 73, 60–69. https://doi.org/10.1016/j.neuropsychologia.2015.04.016.
Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual & Motor Skills, 47(2), 599–604. https://doi.org/10.2466/pms.1978.47.2.599.
Wang, C. J., Geng, F. J., Yao, Y., Weng, J., Hu, Y. Z., & Chen, F. Y. (2015). Abacus training affects math and task switching abilities and modulates their relationships in chinese children. PLoS One, 10(10), 15. https://doi.org/10.1371/journal.pone.0139930.
Wang, Y., Pei, D., & Cui, X. (2017). Pseudo-spherical normal Darboux images of curves on a lightlike surface. Mathematical Methods in the Applied Sciences, 40(18), 7151–7161. https://doi.org/10.1002/mma.4519.
Wechsler, D. (1997). Wechsler Adult Intelligence Scale (third edition). San Antonio, TX: The Psychological Corporation.
Wei, W., Yuan, H. B., Chen, C. S., & Zhou, X. L. (2012). Cognitive correlates of performance in advanced mathematics. British Journal of Educational Psychology, 82(1), 157–181. https://doi.org/10.1111/j.2044-8279.2011.02049.x.
Wu, T. H., Chen, C. L., Huang, Y. H., Liu, R. S., Hsieh, J. C., & Lee, J. J. S. (2009). Effects of long-term practice and task complexity on brain activities when performing abacus-based mental calculations: A PET study. European Journal of Nuclear Medicine & Molecular Imaging, 36(3), 436–445. https://doi.org/10.1007/s00259-008-0949-0.
Yamada, F. (1998). Frontal midline theta rhythm and eyeblinking activity during a VDT task and a video game: Useful tools for psychophysiology in ergonomics. Ergonomics, 41(5), 678–688. https://doi.org/10.1080/001401398186847.
Zhang, Y., Chen, C., Liu, H., Cui, J., & Zhou, X. (2016). Both non-symbolic and symbolic quantity processing are important for arithmetical computation but not for mathematical reasoning. Journal of Cognitive Psychology, 1–18. https://doi.org/10.1080/20445911.2016.1205074.
Zhou, X., & Cheng, D. (2015). When and why numerosity processing is associated with developmental dyscalculia. In S. Chinn (Ed.), The Routledge international handbook of dyscalculia and mathematical learning difficulties (pp. 78–89). New York: Routledge.
Zhou, X., Wei, W., Zhang, Y., Cui, J., & Chen, C. (2015). Visual perception can account for the close relation between numerosity processing and computational fluency. Frontiers in Psychology, 6(1364), 1364. https://doi.org/10.3389/fpsyg.2015.01364.
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This research was supported by three grants from the Natural Science Foundation of China (31,671,151, 31,600,896, and 31,521,063), the 111 Project (BP0719032), and a grant from the Advanced Innovation Center for Future Education (27900–110,631,111).
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Highlights
1) No studies have shown the advantage of non-symbolic number sense for children skilled in mental abacus.
2) Children skilled in mental abacus had better non-symbolic number sense than the controls after controlling for age, gender, general cognitive processing and even arithmetic performance.
3) A mediation model showed that the non-symbolic number sense partially mediated group difference (mental abacus group vs. controls) in symbolic arithmetic.
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Cui, J., Xiao, R., Ma, M. et al. Children skilled in mental abacus show enhanced non-symbolic number sense. Curr Psychol 41, 2053–2066 (2022). https://doi.org/10.1007/s12144-020-00717-0
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DOI: https://doi.org/10.1007/s12144-020-00717-0